Cepheid Variables

Written by User 1

Last Updated: January 17, 2011, 10:12 pm (UTC)
Originally created on January 17, 2011

Most stars in the night sky shine at more or less the same brightness for centuries. One example of such a star is the sun maintaining a relatively constant absolute visual magnitude of 4.83. Other stars are less stable in their brightness which may vary by factors of several hundred or thousand. These are variable stars. Variable stars may be categorized by how they vary. RR Lyrae stars and Cepheids are both categories of variable stars which have repeating cycles of variation showing little to no change from the previous cycle. Cepheid variables are far brighter than RR Lyrae stars and may be observed in distant galaxies. They also exhibit a period-luminosity relation which help to determine their distance making them invaluable resources in mapping the visible universe.

With Cepheid variables, the brighter the star, the longer it takes to complete a cycle. The exact relation depends on the metallicity of the star which categorize them into Population I and Population II. Population I stars are generally found closer to the galactic plane and high relatively high concentrations of metals compared to Population II stars which are found around the galactic halo. Note that Population II Cepheids are also known as W Virginis Cepheids as opposed the Population I designation as classical Cepheids. Categorizing the stars may be done by analyzing absorption lines through spectroscopy. In general Population I Cepheids are brighter than Population II Cepheids with the same period.

The following relations may be used to determine the brightness of a Cepheid variable. Note that these relations are an overall average for Cepheids and variations between stars do exist.

Population I: M = -2.81 logP - 1.43
Population II: M = -2.81 logP + 0.15

M : Mean absolute visual magnitude
P : Period of variation in days

Delta Cepheid is the star which was first identified as a Cepheid. It is a Population I star with a period of 5.37 days. Using the first relation obtains a mean visual absolute magnitude of -3.48.

M = -2.81 log5.37 - 1.43 = -3.48

The value obtained by parallax using the Hubble Space Telescope is -3.47. This is an error of under one percent in luminosity, a more than acceptable value. However, the relation is not always this accurate.

The most famous Cepheid in the night sky is Polaris. Despite its high galactic latitude, it is considered a Population I Cepheid with a relatively high metal concentration of 112% of that of the sun. It has a period of 4.0 days, a value which has been increasing by 8 seconds a year since 1900. Putting that into the relation returns a mean visual absolute magnitude of -3.12.

M = -2.81 log4.0 - 1.43 = -3.12

The official value, determined by parallax, is -3.63 leaving the obtained value with a 0.51 magnitude error which is an error of about 60%, a significant error in terms of factor. However, with stars varying in magnitude by billions of times, this ends up being a decent estimate when no others are available.

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